J. Aust. Math. Soc.
79 (2005), 95112

Bounds and quotient actions of innately transitive groups

John Bamberg
School of Mathematics and Statistics
University of Western Australia
35 Stirling Highway
Crawley WA 6009
Australia
john.bam@maths.uwa.edu.au



Abstract

Finite innately transitive permutation groups
include all finite quasiprimitive and primitive
permutation groups. In this paper, results in
the theory of quasiprimitive and primitive groups
are generalised to innately transitive groups,
and in particular, we extend results of Praeger
and Shalev. Thus we show that innately transitive
groups possess parameter bounds which are similar
to those for primitive groups. We also classify
the innately transitive types of quotient actions
of innately transitive groups.

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